By Alonso Peña
This ebook will introduce you to the foremost mathematical versions used to cost monetary derivatives, in addition to the implementation of major numerical versions used to unravel them. particularly, fairness, foreign money, rates of interest, and credits derivatives are mentioned. within the first a part of the ebook, the most mathematical versions utilized in the realm of monetary derivatives are mentioned. subsequent, the numerical tools used to unravel the mathematical versions are offered. ultimately, either the mathematical types and the numerical tools are used to resolve a few concrete difficulties in fairness, foreign money, rate of interest, and credits derivatives.
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Extra resources for Advanced Quantitative Finance with C++
At maturity (T=1 year), A will have the right (but not the obligation) to buy the underlying from B for the strike price K. The payoff at maturity H is: MATH MODEL 1 ALGORITHM 4 STEP 1: INPUT PARAMETERS STEP 2: SIMULATIONS LOOP for i=1:M STEP 3: TIME INTEGRATION LOOP for 1=1:N *Compute GBM formula at each timestep end STEP 4: COMPUTE PAYOFF end STEP 5: COMPUTE DISCOUNTED EXPECTED PAYOFF STEP 6: OUTPUT PREMIUM VALUE THE BENTO BOX TEMPLATE Bento Box template for basic example: European Call Our objective is to calculate the premium of this financial derivative.
In quantitative finance, we encounter various types of PDEs. The most important is the Black-Scholes PDE, which is expressed as follows: w9 w 9 w9 V 6 U6 U9 wW w6 w6 We now consider solving this equation in a rectangular domain in the S and t axes. In the S axis, the domain is [a,b]. In the t axis the domain is [0,T]. This can be written mathematically as the domain : ^> D E @ u > 7 @`. In the case of a European Call, it has a final condition as follows: 9 6 7 PD[ 6 .
We will now take these models as basis to model the underlying of the various asset classes we reviewed and apply a number of numerical methods to implement their calculations efficiently in a computer. In the next chapter, we will concentrate on numerical methods. [ 31 ] Numerical Methods In the previous chapter, we reviewed some of the key mathematical models used to describe the behavior of the underlying assets of financial derivatives. We saw, in particular, how these models are used to describe the future behavior of these assets based on the information we have today.
Advanced Quantitative Finance with C++ by Alonso Peña